Question

A lightbulb manufacturer wants to estimate the total number of defective bulbs contained in all of the boxes shipped by the company during the past week. Production personnel at this company have recorded the number of defective bulbs found in each of 50 randomly selected boxes shipped during the past week. These data are provided down below. Calculate a 95% confidence interval for the total number of defective bulbs contained in the 1000 boxes shipped by this company during the past week. (Round your answers to a whole number.) Calculate the lower and upper limit.

Box	Number Defective
1	1
2	0
3	0
4	0
5	0
6	1
7	0
8	0
9	2
10	0
11	0
12	0
13	0
14	0
15	0
16	0
17	0
18	1
19	1
20	0
21	0
22	1
23	0
24	0
25	0
26	0
27	0
28	0
29	1
30	0
31	0
32	0
33	2
34	0
35	1
36	0
37	0
38	1
39	0
40	0
41	0
42	2
43	3
44	0
45	2
46	0
47	0
48	2
49	0
50	0

   

Answer 1

Box	Number Defective	Increasing order
1	1	0
2	0	0
3	0	0
4	0	0
5	0	0
6	1	0
7	0	0
8	0	0
9	2	0
10	0	0
11	0	0
12	0	0
13	0	0
14	0	0
15	0	0
16	0	0
17	0	0
18	1	0
19	1	0
20	0	0
21	0	0
22	1	0
23	0	0
24	0	0
25	0	0
26	0	0
27	0	0
28	0	0
29	1	0
30	0	0
31	0	0
32	0	0
33	2	0
34	0	0
35	1	0
36	0	0	36
37	0	1
38	1	1
39	0	1
40	0	1
41	0	1
42	2	1
43	3	1
44	0	1	8
45	2	2
46	0	2
47	0	2
48	2	2
49	0	2	5
50	0	3	1
x	f	fx
0	36	0
1	8	8
2	5	10
3	1	3
sum=	50	21
Mean =	21/50
Mean =	0.42
vaiance=	0.42
sd=	sqrt(0.42)
sd=	0.64807407

In the Poisson distribution, then the mean and the variance both are equal .

Here

Mean = 0.42

Standard deviation = 0.64807407

95% confidence interval is given by

95% confidence interval is given by

0.42 1.96 *0.64807407/ sqrt(50)

0.42 0.179637

{0.240363, 0.59963697}

so in 1000 boxes ,number of defective boxes lies between

( 240   ,   600) Answer